A variety of catheters and cannulae are used in ophthalmic surgery to deliver fluid, gas, suction and energy to select regions of the eye. Existing cannulae are typically straight or curved segments of rigid plastic or metal tubing attached to a connector. In the development of advanced surgical methods to treat the eye, it is desired to have cannulae that can access and be advanced into very small structures or channels in the eye to perform minimally invasive procedures. Such microcannulae that access curved or tortuous spaces such as Schlemm's Canal or small blood vessels require a combination of flexibility and “pushability”, while maintaining a diameter in the range of 50 to 350 microns. The present invention describes microcannulae that are constructed with multiple components in a composite design. The composite design allows the microcannula to have varying mechanical and delivery properties that will enable ophthalmic treatments by minimally invasive means.